let $pqr$ be an equilateral triangle, centered at $o.$ a point $x$ is chosen at random inside the triangle. find the probability that $x$ is closer to $o$ than to any of the vertices. (in other words, find the probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$)

Answer:

true

Step-by-step explanation:

cause I’ve done this before

Answer: To find the unit price for each fork, we need to divide the total cost of the box by the number of forks in the box.

The cost of the box is $4.98, and the box contains 96 forks. So the unit price for each fork is:

$4.98 ÷ 96 = $0.051875

Rounding to the nearest cent, the unit price for each fork is $0.05.

Step-by-step explanation:

Using the unitary method, we found that the cost of one fork of brand B is $0.051.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. We typically utilise this technique for maths computations. This method allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.

The worth of many things is supplied in the unitary technique, and we must either determine the value of more or fewer items. To do that, we must first determine the value of a single item by division and then determine the value of further or more items by multiplication.

Given,

The number of forks in a box of brand B = 96

  Price of 96 forks = $4.98

The unit price of brand B = Cost of one fork

Using the unitary method,

96 forks = $4.98

1 fork = $4.98 / 96 = $0.051

Therefore using the unitary method, we found that the cost of one fork of brand B is $0.051.

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Answer:

Step-by-step explanation:

The two numbers that multiply to -140 also have to add to -13, so that means that the larger of the two numbers needs to be negative, and the other number positive.

7 x -20 = -140

7 - 20 = -13

Answer:0.047

Step-by-step explanation: This is actually easy  you need to divide using long division and put the numbers of the division that you use to subtract and then you get the answer.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

Since the diameter of the garden is 42m, the radius is half of that, which is:

r = 42m / 2 = 21m

The circumference of the circular garden is therefore:

C = 2πr = 2π(21m) = 42πm

If the gardener makes 4 rounds of the fence, he will need to purchase 4 times the circumference of the garden in barbed wire. Therefore, the length of barbed wire he needs to purchase is:

4 x 42πm = 168πm

This is approximately equal to 527.79m, if we use the value of π to two decimal places.

Answer:

528 M

Step-by-step explanation:

CIRCUMFERENCE OF GARDEN= 2 pi r

r=42/2 =21

circumference = 2x (22/7) x21

=132 m

To make 4 rounds= 4 x 132 = 528m

Answer:

13x-16

Step-by-step explanation:

I am assuming that you mean 5*(2 + 2x − 3) − (2*2 − 3x + 7).

That equals 10x-5+3x-11=13x-16

The cosine equation of the function is y = 5cos (x + π/4) + (4).

What is the cosine function?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

y = A cos (Bx - C) + D

A (amplitude) = max - D

B = Period/2π  --->   Period is the distance from max to next max

C = B · Phase Shift  ---> Phase shift is the distance from the y-axis to the max

D (vertical shift) = (max + min)/2

Maximum = 9, minimum = -1

A = (maximum-minimum)/2 = (9 - -1)/2 = 10/2 = 5

Vertical shift = maximum - A = 9 - 5 = 4

The maximum occurs at x = -π/4, and

for the original function (without shift), the maximum occurs at x = 0

So, the horizontal shift = 0 - (-π/4) = π/4

Hence, the cosine equation of the function is y = 5cos (x + π/4) + (4).

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Answer:

===================================================

Work Shown:

x = amount invested at 9%

y = amount invested at 3%

x+y = 2300 invested total, which solves to y = 2300-x

0.09x+0.03y = 189 dollars of total profit

Applying substitution to solve.

0.09x+0.03y = 189

0.09x+0.03(y) = 189

0.09x+0.03(2300-x) = 189

0.09x+69-0.03x = 189

0.06x+69 = 189

0.06x = 189-69

0.06x = 120

x = 120/0.06

x = 2000

y = 2300-x = 2300-2000 = 300

The solution as an ordered pair is (x, y) = (2000, 300)

Therefore, $2000 was invested at 9%, and $300 was invested at 3%.

The solution to the given inequality w > 2w - 9 is w < 9.

Inequality is defined as mathematical pieces of information that have a minimum of two terms including variables or numbers that are not equal.

The "inequality" is given in the question, as follows:

w > 2w - 9

We have to solve the above inequality for w.

⇒ w > 2w - 9

Rearrange the term of variable w in the above inequality,

⇒ w - 2w > - 9

Apply the subtraction operation and solve for w:

⇒ - w > - 9

Multiply the negative sign and flip the sign of inequality:

⇒ w < 9

Thus, the solution to the given inequality is w < 9.

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Based on the graph, we can see that the relationship between the number of stuffed animals and the number of action figures is proportional since the line passes through the origin (0, 0), which is a characteristic of proportional relationships.

Mathematical relationships between two variables that have a constant multiple of one another are known as proportional relationships. This implies that when one variable rises or falls by a particular factor, the other variable rises or falls by the same amount as well.

In other words, a straight line on a graph that runs through the origin (0, 0) can be used to illustrate a proportionate connection. This is due to the fact that they are proportional, therefore when one variable is equal to zero, the other variable must likewise be zero.

To graph the linear relationship between the number of stuffed animals, x, and the number of action figures, y, we can use the two given data points: (20, 15) and (60, 45).

First, we can find the slope of the line that passes through these two points using the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (20, 15) and (x2, y2) = (60, 45)

slope = (45 - 15) / (60 - 20) = 30 / 40 = 0.75

Next, we can use the point-slope form of the equation of a line to write the equation of the line that passes through the two points:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) = (20, 15)

y - 15 = 0.75(x - 20)

y - 15 = 0.75x - 15

y = 0.75x

Now we can graph the line by plotting the two given points and drawing a straight line passing through them:

Linear relationship graph

Based on the graph, we can see that the relationship between the number of stuffed animals and the number of action figures is proportional, since the line passes through the origin (0, 0), which is a characteristic of proportional relationships.

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Answer:

he probability of Violeta pulling out a green marble is 0.3 or 30%.

Step-by-step explanation:

he probability of pulling out a green marble is the number of green marbles divided by the total number of marbles in the bag:

P(green marble) = number of green marbles / total number of marbles

In this case, there are 6 green marbles and 14 pink marbles, so the total number of marbles is:

total number of marbles = 6 + 14 = 20

Therefore, the probability of pulling out a green marble is:

P(green marble) = 6 / 20 = 3/10 = 0.3

So the probability of Violeta pulling out a green marble is 0.3 or 30%.

Answer:its 1.4>1.3

Step-by-step explanation:I THINK ITS 1.4>1.3

The speed of the satellite around the earth in miles per hour is 8659.09 miles per hour.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is important to determine the quantity of any object.

A same quantity can have more than one type of measurement which can be converted to each other.

Given,

Speed of the satellite in feet per second = 12700 feet per second (ft/s)

We have,

5280 feet = 1 mile

1 feet = 1/5280 mile

12700 feet = 12700/ 5280 miles

Also,

60 minute = 1 hour

1 minute = 1/60 hour

60 seconds = 1 minute = 1/60 hour

1 second = 1/3600 hour

12700 feet per second =  12700/ 5280 miles ÷ 1/3600 hour

                                      = 8659.09 miles per hour.

Hence the speed converted is 8659.09 miles per hour.

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Answer:

middle set of data

Step-by-step explanation:

The scatterplot shows the weakest positive linear association is (a)

From the question, we have the following parameters that can be used in our computation:

The graphs

A good line of best fit would have equal number of points on either sides

Using the images as a guide, we can see that:

Graph (a) and (b) have a positive linear association while graph (a) have the least number of points that appear to be on a straight line

This means that the line with the weakest is (a)

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Statements B , D and E are True.

Statements A and C are False.

The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

A. Prism A and C have the same volume. - False

The volume of Prism A is 5 x 6 x 4 = 120 cubic cm, while the volume of Prism C is 7 x 3 x 5 = 105 cubic cm.

B. Prism B has a greater volume than Prism C. - True

The volume of Prism B is 8 x 4 x 3 = 96 cubic cm, while the volume of Prism C is 7 x 3 x 5 = 105 cubic cm.

C. Prism B has the least volume. - False

The volume of Prism A is 5 x 6 x 4 = 120 cubic cm, which is greater than the volume of Prism B.

D. The volume of Prism A is 120 cubic centimeters. - True

As calculated above, the volume of Prism A is 120 cubic cm.

E. The volume of Prism C is less than the volume of Prism A. - True

As calculated above, the volume of Prism C is 105 cubic cm, which is less than the volume of Prism A.

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The statement if Cathy does not love horses, she is not a gambler is valid.

Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).

We are given;

The two arguements

Now,

A). The argument is valid. This is an example of the disjunctive syllogism, which is a valid form of argument. If we have a disjunction "A or B", and we know that A is false, then we can conclude that B must be true. In this case, "she will go to school or she will get a job" is the disjunction, and "she will not get a job" tells us that "she will not get a job" is true. Therefore, we can conclude that "she will go to school" must be true.

B). The argument is invalid. This is an example of the fallacy of affirming the consequent. The conditional statement "if Cathy is a gambler, then she lives in Marine" tells us that if Cathy is a gambler, then she lives in Marine. However, it does not tell us anything about whether Cathy is a gambler or not. The fact that "Cathy lives in Marine and she loves horses" does not give us any information about whether Cathy is a gambler or not.

Therefore, by the given conditions answer "if Cathy does not love horses, she is not a gambler" will be valid

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Square root of 8 plus square root of 1 equal 3.82842712

Algebraic integers

The square roots of an integer are algebraic integers —more specifically quadratic integers. The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors.

⇒ 3.8 rounded.

⇒ = 3.82842712

Hence, Square root of 8 plus square root of 1 equal 3.82842712

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Answer:

[tex]x < -3\text{ or }x > 3[/tex]

Step-by-step explanation:

[tex]|1-2x|-4 > 1\\|1-2x| > 5\\\\1-2x > 5\\-2x > 6\\x < -3\\\\1-2x < -5\\-2x < -6\\x > 3[/tex]

Answer:

Answer:

See attached image and explanation below

Step-by-step explanation:

For the first table:
The cumulative frequency for each class interval is obtained by adding that class frequency to the sum of all frequencies less than that class interval

So the table will look as in the first image attached

The second table talks about cumulative relative frequency and it uses the same technique as above but we are dealing with relative rather than absolute frequencies

The second image shows the correct values

Your relative frequency table (the third image you posted) is correct

There are 840 ways for Yunseol to draw four cards from Ms. Q's deck, such that no two cards have the same color.

From the question, we have the following parameters that can be used in our computation:

Colors = (1, 2, 3, 4, 5, 6, and 7).

To solve this problem, we can use the multiplication principle of counting.

We need to choose one card from each of the four colors, we use the following:

To count the total number of ways to draw four cards, we multiply the number of choices at each stage:

Total number of ways = 7 × 6 × 5 × 4 = 840

Hence, there are 840 ways for Yunseol to draw four cards

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On solving the provided question we can say that at a simple 12% annual percentage rate, it would take approximately 6 years for capital to double.

In mathematics, a ratio or number expressed as a percentage of 100 is called a percentage. Also occasionally used are the acronyms "pct.," "pct," and "pc." Nonetheless, the percentage symbol "%" is widely used to represent it. The % quantity is dimensionally empty. Basically, percentages are fractions when the denominator is 100.

The annual rate of return is 12%, so we can calculate:

Time to double = 72 / 12 = 6 years

Therefore, at a simple 12% annual rate, it would take approximately 6 years for capital to double.

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The correct question is -

How long does it take for capital to double at a simple 12% annual rate?

Answer:

y = (12 / (25/12)^7) * (25/12)^x

Step-by-step explanation:

To write an exponential model given two points, we can use the general form of an exponential function:

y = ab^x

where y is the dependent variable, x is the independent variable, b is the base or growth factor, and a is the initial value when x = 0.

Using the two given points, we can form a system of equations:

12 = ab^7 (1)

25 = ab^8 (2)

Dividing equation (2) by equation (1), we get:

25/12 = b^(8-7) = b

So the base of the exponential function is b = 25/12.

To find the initial value a, we can substitute b into either of the original equations. Let's use equation (1):

12 = a(25/12)^7

Simplifying, we get:

a = 12 / (25/12)^7

Therefore, the exponential model that fits the given points is:

y = (12 / (25/12)^7) * (25/12)^x

The linear programming model that can be used to determine the number of units of each model in order to maximize the profit is x2 <= 280 (Lady-Sport Frames), 2 x1 + 2.5 x2 <= 1000 (Assembly & Test).

When a linear function is exposed to various constraints, it is maximised or reduced using the mathematical modelling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.

A linear programming problem can be solved by determining the best value.

a)Let x1 be number of EZ-Riders produced.

Let x2 be number of Lady-Sports produced.

The Objective is to maximize the profit contribution:

Max 2,400 x1 + 1,800 x 2

The Constraints are: Engine Manufacturing Time <= 2100 hours

Lady-Sport Frames <= 280 frames

Assembly & Test <= 1000 hours

6 x1 + 3 x2 <= 2100 (Engine Manufacturing)

x2 <= 280 (Lady-Sport Frames)

2 x1 + 2.5 x2 <= 1000 (Assembly & Test)

We also need bounds x1 and x2 => 0.

So the full model is:

Max 2,400 x1 + 1,800 x2

Subject to 6 x1 + 3 x2 <= 2100 (Engine Manufacturing)

x2 <= 280 (Lady-Sport Frames)

2 x1 + 2.5 x2 <= 1000 (Assembly & Test)

x1 => 0, x2 => 0

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The required turtle's speed is 12/5 miles per hour, as of the given condition.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
To find the turtle's speed in miles per hour, we need to convert the fraction of miles traveled in a fraction of an hour to miles per hour.

First, we can simplify the fraction 3/5 by dividing the numerator and denominator by 1/4,

speed = distance/time

Substitute the value in the above expression,
Speed = 3/5 / [1/4]
Speed = 12/5

Therefore, the turtle's speed is 12/5 miles per hour.

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This expression gives the mean number of coupons you will need to collect before you have a complete set, given that each coupon obtained is equally likely to be any one of the c types.

In general, probability is a measure of the likelihood that a certain event or outcome will occur. It is a branch of mathematics concerned with analyzing and quantifying uncertainty. In formal terms, the probability of an event is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. Probabilities between 0 and 1 represent the degree of uncertainty associated with the event.

Here,

The probability that the first n coupons collected do not form a complete set can be found as follows:

Let S be the event that the first n coupons do not form a complete set, and let Ci be the event that the i-th coupon collected is a new type (i.e., a coupon of a type that has not been collected before).

Then, the event S can be expressed as the intersection of the events C1, C2, ..., Cn, where each Ci is independent of the others and has probability (c-i+1)/c of occurring. This is because there are c-i+1 types of coupons remaining after i-1 types have been collected, and each of these types is equally likely to be the next coupon collected.

So, the probability of S can be calculated as:

P(S) = P(C1 ∩ C2 ∩ ... ∩ Cn) = P(C1) × P(C2) × ... × P(Cn)

= (c-1)/c × (c-2)/c × ... × (c-n+1)/c

= Π(i=1 to n) (c-i+1)/c

To deduce an expression for the mean number of coupons you will need to collect before you have a complete set, let X be the random variable representing the number of coupons collected until a complete set is obtained. Then, the expected value of X can be calculated using the formula:

E(X) = Σ(k=1 to c) P(X ≥ k)

This formula sums the probabilities of all possible numbers of coupons collected until a complete set is obtained, weighted by their respective probabilities.

Note that P(X ≥ k) is the probability that a complete set has not been obtained after k-1 coupons have been collected, which is equal to the probability of the event S above. So, we can substitute the expression for P(S) into the formula for E(X) to get:

E(X) = Σ(k=1 to c) P(X ≥ k)

= Σ(k=1 to c) Π(i=1 to k-1) (c-i+1)/c

= Σ(k=1 to c) Π(i=0 to k-2) (c-i)/c

= Σ(k=0 to c-1) Π(i=0 to k-1) (c-i)/c (by changing the index of summation)

= Σ(k=0 to c-1) (c-k)/cˣ

= c Σ(k=0 to c-1) (1/c)ˣ - Σ(k=0 to c-1) (k/c)ˣ

= c (1 - (1/c)ˣ)/(1 - 1/c) - B(c, 1/c)

where B(c, 1/c) is the sum of the first c terms of the series (k/c)ˣ.

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The number of each denomination is: 13 of the $10-dollars bills.

Let x be number of the $20 dollars bills. Then, the number of the $10 dollars bills is (x+2), according to the condition.

The money equation will then be:

20x + 10*(x+2) = 350

Now, solve for x.  

20x + 10x + 20 = 350

30x = 350 -20

30x = 330

x = 330/30

x = 11

So, 11 of the $20 dollars bills and 11 +2 = 13 of the $10-dollars bills.

Full question "Part of the proceeds from a garage sale was ​$350 worth of ​$10 and ​$20 bills. If there were 2 more $10 bills than $20 bills, find the number of each denomination.

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Answer:$728

Step-by-step explanation: 4 percent increase= 104% which is x1.04

=700*1.04  

Answer:

We are aware of the equation.

Equation 1 reads (fg)(x) = f(x) * g(x).

Hence, we can resolve it as follows:

Given equation: equation 2 (fg)(x) = 3x (x2 + 5)

Equation 3 is obtained by comparing equations 1 and 2, as follows:

"f(x)*g(x)" equals "3x (x2 + 5" - The equation 3 that is provided: f(x) = x2 + 5

When we change equation 3 to read f(x) = x2 + 5, we get:

(x2 + 5) * g(x) = 3x (x2 + 5)

See what both equations have in common; it is (x2 + 5)

The result of dividing both sides by x2 + 5 is:

g(x) = 3x

G(x) will therefore have a value of 3x.

From the above equation given in the question , we get that g(x)  have a value of 3x.

We are aware of the equation.

Equation 1 reads (fg)(x) = f(x) * g(x).

Hence, we can resolve it as follows:

Given equation: equation 2 (fg)(x) = 3x (x2 + 5)

Equation 3 is obtained by comparing equations 1 and 2, as follows:

"f(x)*g(x)" equals "3x (x2 + 5" - The equation 3 that is provided: f(x) = x2 + 5

When we change equation 3 to read f(x) = x2 + 5, we get:

(x2 + 5) * g(x) = 3x (x2 + 5)

See what both equations have in common; it is (x2 + 5)

The result of dividing both sides by x2 + 5 is:

g(x) = 3x

G(x) will therefore have a value of 3x.

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